It appears to be some kind of unofficial award ceremony at 3 minutes onwards, three soldiers stand infront of a makeshift table with a draped flag as a table cloth. An officer removes a ring from his top right pocket, and proceeds to place the ring onto the finger of the soldier. A few salutes and a shot of schnapps... And the other soldiers congratulate the receiver.
Unfortunately the film is without sound but I think Mike and SpitfireVb hit the nail on the head. A far distance marriage. "Only" the groom is getting the ring (none of the other two soldiers got a ring - as they are groomesmen). Therefore the groom is signing the mariage certificate as does the officer as marriage registrar. And as Spitfire Vb stated, here are wedding rings worn on the right hand. Regards,